There is but one PDS in $\mathbb{Z}^{3}$ inducing just square components
Combinatorics
2018-02-08 v9
Abstract
It is known that in the unit distance graph of the lattice there exists a dominating set with -cycles as sole induced components and each vertex of having a unique neighbor in . We show is unique.
Cite
@article{arxiv.1706.08165,
title = {There is but one PDS in $\mathbb{Z}^{3}$ inducing just square components},
author = {Italo J. Dejter and Luis R. Fuentes and Carlos A. Araujo},
journal= {arXiv preprint arXiv:1706.08165},
year = {2018}
}
Comments
22 pages, 14 figures